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The Mage thows a fireball, the fireball is so large and powerful it hits the castle walls. The castle walls are fairly large and heavy built from large boulders, it makes a crack in the wall and pushes a stone out. In this case the fireball accelerates to full speed after the spell cast and decelerates to a near halt when it hits the wall.

From what little physics i know the force that hits the wall equals the weight times the acceleration. The acceleration is slow enough for a common man over a 50 yard distance to avoid it. Meaning the weight of the ball has to be fairly high to break down a common castle wall.

So if the fireball is fairly heavy and according to newtons law of motion "To every action there is always opposed an equal reaction", the mage has to throw him self several meters back to propel the fireball towards the wall. But this is the fun part, he just stand as if he had just thrown a tennis ball.

How could this be explained in otherways except "because magic"?

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    $\begingroup$ Here's a real-world example for you to think about: I throw a brick of C4 at the castle wall. When it hits, the explosion throws rubble great distances. Does this mean the C4 must have been really heavy, and that I pushed myself back many yards when I threw it? $\endgroup$ – 2012rcampion May 11 '15 at 14:38
  • $\begingroup$ So you means that the fireball explodes on impact instead of being considered heavy in weight, like a grenade ? $\endgroup$ – Magic-Mouse May 11 '15 at 14:39
  • $\begingroup$ That was always my interpretation. There is another point, which is that $F=ma$ applies to values at a particular moment: the force a weight applies to the wall is proportional to the rate at which the wall is slowing it down, not to the acceleration of the weight at any earlier part of the weight's trajectory. $\endgroup$ – 2012rcampion May 11 '15 at 14:44
  • $\begingroup$ No but the speed it is accelerated to is near instantaneous the same way the wall slows it down near instantaneous when hit. $\endgroup$ – Magic-Mouse May 11 '15 at 14:48
  • $\begingroup$ I was referring to your phrase "The acceleration is slow enough..." where it seems to me that you intend "The speed is slow enough..." $\endgroup$ – 2012rcampion May 11 '15 at 14:49
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As @2012rcampion points out, the fireball doesn't have to be heavy, it just has to have a lot of potential energy, like a fiery explosion.

It's not the weight of the object (like a wrecking ball), but the force of the blast that does the damage.

If you don't want to go with that then think of this: where does the fireball come from? It's not like the mage is keeping a little ball of fire in his pocket to pull out and throw. Instead he's summoning it from somewhere else, like the energy of the universe. So in effect, he's not throwing the ball, just summoning it into being at the point of his hand and traveling at velocity toward the wall. He's not throwing it, the universe is throwing it, and he's just directing it. So there would be no recoil on him. This is true whether it is weighty or just explosive. It would also allow him to throw it further and with more force than his own physical strength would allow.

But a heavy fireball makes little sense, while an explosive fireball does.

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  • $\begingroup$ I will never be able to forget the image of a universe throwing a fire ball... or fire ball. $\endgroup$ – HadesHerald May 12 '15 at 1:51
  • $\begingroup$ A large amount of energy instantiating itself at a point in front of you and then accelerating in a direction opposite your standing means you should feel a push-back. Whether it's enough to knock you backwards is a question of power. $\endgroup$ – Muhammad Abdul-Rahim May 13 '15 at 19:34
  • $\begingroup$ @MariM if a bird appears in front of me and accelerates away from me it's not really going to push me back, because I'm not propelling it and never touch it. This is similar. If anything it might pull me forward due to low pressure because of the fire ball moving away and consuming oxygen. $\endgroup$ – AndyD273 May 14 '15 at 23:36
  • $\begingroup$ If the bird suddenly appears in front of you and is large enough and fast enough to destroy a wall you will feel it. If I'm standing next to somebody firing a gun, depending on the size of the gun, I will feel a force even if I'm not the one in direct contact with it. $\endgroup$ – Muhammad Abdul-Rahim May 15 '15 at 12:01
  • $\begingroup$ @MariM I suppose it depends on the method. We went to a reenactment thing where they fired off a 4 inch cannon as a demonstration of what kind of damage one of those pieces could do. There was maybe a bit of over pressure from the powder going off, but it wasn't very noticeable. Like being close to a bass speaker for an instant. You definitely wouldn't get any kind of recoil like the question was implying. Here's a big gun being fired. The explosive shell could probably knock down a wall. The people next to it don't seem to be buffeted much. $\endgroup$ – AndyD273 May 15 '15 at 14:13
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The fireball could be partially or completely self-propelled, like a hand-launched drone aircraft.

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Once airborne the magical fireball could rocket itself straight into the stone wall, picking up speed and momentum. It could even grow in size and mass during flight, adding to the force it will apply to the wall. The self-propelled fireball could also course correct to aim for imperceptible weak spots in the construction of the wall, adding to the damage. (And it could still explode as @AndyD273 suggested.)

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I usually tend to imagine it like there being several dimensions, and being magic the ability of mess with those dimensions. Therefore, you could use the kinetic energy of some particles, living in that magical dimension and trespass them to the normal one, not violating any Newtonian Law.

Another alternative is using the well-known formula of $E=mc^2$, and being the mage able to convert the mass of oxygen into energy, both thermic and kinetic.

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